Method of fundamental solutions and a high order continuation for bifurcation analysis within Föppl-von Karman plate theory

Radial point interpolation‐Chebychev method with asymptotic numerical method for nonlinear buckling analysis of graphene oxide powder‐reinforced composite beams

“…This could mean, for example, a transition from a stable equilibrium to an unstable one, or the emergence of new oscillatory behavior. 20,22,23,29,[31][32][33][34][35][36][37][38][39][40] Bifurcation analysis has applications in many areas of science and engineering. For example, in physics, bifurcation analysis can be used to understand the behavior of complex systems such as fluid flows.…”

Efficient resolution of incompressible Navier–Stokes equations using a robust high‐order pseudo‐spectral approach

“…$$$$ \left\{\begin{array}{c}\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0\\ {}u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}=-\frac{\partial p}{\partial x}+\frac{1}{\mathit{\operatorname{Re}}}\Delta u\\ {}u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}=-\frac{\partial p}{\partial y}+\frac{1}{\mathit{\operatorname{Re}}}\Delta v\end{array}\right., $$$$ where $$$ u $$$ and $$$ v $$$ are the velocity components in the $$$ x $$$‐ and $$$ y $$$‐directions respectively, $$$ p $$$ is the pressure and $$$ \mathit{\operatorname{Re}} $$$ is the nonnegative Reynolds number. The above nonlinear equations can be easily solved using several mesh‐free approaches that existing in the literature such as References 10,18,33,37‐40. Few papers have been published basing on a strong form of vorticity‐stream function formulation where the cited approaches find difficulty in managing hermit‐type bo...…”

“…The use of such a numerical approach could be limited or motivated by testing this factor. Among the best‐known meshless methods in the literature, we find Smooth Particle Hydrodynamics (SPH), 6‐8 Moving Least Squares (MLS) approximation, 2,9‐13 Reproducing Kernel Particle Method (RKPM), 14 Element‐Free Galerkin Methods (EFGM), 15 Taylor meshless method, 16 and Method of Fundamental Solutions (MFS), 17,18 Radial Basis Function 19‐21 …”

“…The use of such a numerical approach could be limited or motivated by testing this factor. Among the best-known meshless methods in the literature, we find Smooth Particle Hydrodynamics (SPH), [6][7][8] Moving Least Squares (MLS) approximation, 2,[9][10][11][12][13] Reproducing Kernel Particle Method (RKPM), 14 Element-Free Galerkin Methods (EFGM), 15 Taylor meshless method, 16 and Method of Fundamental Solutions (MFS), 17,18 Radial Basis Function. [19][20][21] Regarding incompressible fluid flows, the need for careful software to treat the coupling between pressure and velocity fields in (N-S)-equations leads to develop mathematical models and numerical simulations as prediction means.…”

Spectral Chebyshev method coupled with a high order continuation for nonlinear bending and buckling analysis of functionally graded sandwich beams

“…In addition, the use of beam model, which takes into account the nonlinear term neglected in several works of the literature, permits us to analyze buckling and bending problems by using the classical Timoshenko model and to handle the boundary conditions that several works could not to take into account. The HOCM has been coupled with meshless methods successfully in several works such as the moving least squares (MLS), 14,15 the method of fundamental solutions (MFS), [16][17][18] and the radial point interpolation method (RPIM). 19,20 The SCDQM has been also used in several works and showed its ability and efficiency in the computation of FG porous plates reinforced by graphene platelets.…”